CPT-invariant modification of the 1932 Majorana equation

Establish whether a modification of the infinite-component Majorana equation for arbitrary spin exists that renders the wave operator invariant under CPT transformations, and, if so, construct such a CPT-invariant formulation.

Background

Within the infinite-dimensional representation framework used by Majorana, the transformation required to implement CPT symmetry (specifically, mapping Γ to −Γ) does not exist due to the structure of the boosts and the spectrum of γ0, implying the wave operator is not CPT invariant as formulated.

The author explicitly states that it cannot be ruled out that a modified version of the Majorana theory might achieve CPT invariance, identifying a concrete unresolved question about the existence and form of such a modification.

References

However, it cannot be a priori ruled out that Majorana's theory can be modified to make it invariant under the action of CPT symmetry.

— The 1932 Majorana equation: a forgotten but surprisingly modern particle theory (2404.01357 - Nanni, 1 Apr 2024) in Section 2, The Majorana Formalism (CPT symmetry paragraph)